The invention relates to the field of continuous phase modulation communications systems. More particularly, the present invention relates to carrier phase tracking for continues phase modulations communications systems, such as Gaussian minimum shift keying communications systems having small bandwidth time products.
In synchronous digital data communication systems, the carrier phase and symbol timing of the received signal must be acquired and tracked by the receiver in order to respectively demodulate the received signal and to recover the transmitted data from the received signal. Typically, receivers require carrier phase tracking for signal demodulation and symbol time tracking for data detection for generating received data streams.
Continuous phase modulation (CPM) provides a class of digital phase modulation signals that have a constant envelope. The spectral occupancy of a CPM signal can be controlled or tailored to the available bandwidth of a transmission channel. The constant envelope CPM signals allow saturated power amplifier operation for maximum power efficiency. The use of CPM signals in communications systems can potentially achieve significant improvement in both power and spectral efficiency over other conventional modulation techniques, at the cost of a moderate increase in receiver complexity. Bit error rate reduction has en achieved using trellis CPM demodulation with ideal synchronization. There is a continuing need to develop hardware implementation of the symbol time and carrier phase synchronizers that provides required tracking functions for the coherent CPM receiver. Often, symbol time tracking and carrier phase tracking limit the performance of CPM systems.
A particular type of CPM system is a Gaussian minimum shift keying (GMSK) system where a data sequence is precoded and the precoded data symbols are used for continuous phase modulation. The GMSK received signals are filtered using Laurent filters and samplers for providing data samples subject to trellis demodulation for generating an estimate of the data sequence. Carrier phase tracking loops are used for demodulating the received signal by tracking the carrier phase, and symbol time tracking loops are used for synchronized sampling of Laurent matched filter signals for generating the data samples that used to generate estimates of the transmitted bit stream using trellis demodulation. These carrier phase and symbol time tracking loops are often referred to as synchronizer. These synchronizers often lose track during noisy communications.
A binary continuous phase modulation signal can be described by complex envelop equations.                               z          ⁡                      (            t            )                          =                ⁢                  Re          ⁡                      (                                                            z                  b                                ⁡                                  (                  t                  )                                            ⁢                              ⅇ                                  j2π                  ⁢                                      xe2x80x83                                    ⁢                                      f                    c                                    ⁢                  t                                                      )                                                                        z            b                    ⁡                      (            t            )                          =                ⁢                                            2              ⁢                                                E                  b                                /                T                                              ⁢                      ⅇ                          jφ              ⁡                              (                                  t                  ,                  α                                )                                                                                      φ          ⁡                      (                          t              ,              α                        )                          =                ⁢                  π          ⁢                      xe2x80x83                    ⁢          h          ⁢                                    ∫                              -                ∞                            t                        ⁢                                          ∑                                  n                  =                  0                                                  N                  -                  1                                            ⁢                              xe2x80x83                            ⁢                                                α                  n                                ⁢                                  f                  ⁡                                      (                                          t                      -                      nT                                        )                                                  ⁢                                  xe2x80x83                                ⁢                                  ⅆ                  t                                                                                            =                ⁢                  π          ⁢                      xe2x80x83                    ⁢          h          ⁢                                    ∑                              n                =                0                                            N                -                1                                      ⁢                                          α                n                            ⁢                              g                ⁡                                  (                                      t                    -                    nT                                    )                                                                        
The term zb(t) is called the complex envelope of the CPM signal, fc is the carrier frequency, Eb is the bit energy, T is the bit duration, and N is the transmitted data length in bits, xcex1=(xcex10xcex11 . . . xcex1Nxe2x88x921,)xcex1i ∈{xc2x11}, represents one of 2N equally probable data sequences. The parameter h is the modulation index, f(t) is the pulse response of the smoothing filter in the CPM modulator, and g(t) is the CPM phase response defined in terms of the f(t) pulse response.       g    ⁡          (      t      )        =            ∫              -        ∞            t        ⁢                  f        ⁡                  (          s          )                    ⁢              xe2x80x83            ⁢              ⅆ        s            
The pulse response f(t) is limited to the time interval [0,LT] for some integer L and having the properties that f(t)=f(LT-t) and g(LT)=1. The pulse amplitude modulation (PAM) representation of signal CPM envelope is well known. Laurent has shown that the complex envelope zb(t) can be expressed as a double summation.             z      b        ⁡          (      t      )        =                              2          ⁢                                    E              b                        /            T                              2        ⁢                  ∑                  k          =          0                          L          -          1                    ⁢              xe2x80x83            ⁢                        ∑                      n            =            0                                N            -            1                          ⁢                  xe2x80x83                ⁢                              a                          k              ,              n                                ⁢                                    h              k                        ⁡                          (                              t                -                kT                            )                                          
In this PAM representation of the baseband CPM signal envelope, also referred to as the Laurent decomposition, the ak,n values are known as pseudo data symbols and are related to the modulated data symbols generally by a pseudo data symbol equation.       a          k      ,      n        =      exp    ⁡          (              jh        ⁢                  xe2x80x83                ⁢                  π          ⁡                      [                                                            ∑                                      m                    =                    0                                    n                                ⁢                                  xe2x80x83                                ⁢                                  α                  m                                            -                                                ∑                                      i                    =                    0                                                        L                    -                    1                                                  ⁢                                  xe2x80x83                                ⁢                                                      α                                          n                      -                      i                                                        ⁢                                      β                                          k                      ,                      i                                                                                            ]                              )      
In the pseudo data symbol equation, for all k, 0xe2x89xa6k,xe2x89xa62L-1,xcex2ki, and xcex2ki is a 0 or 1 digit in the binary expansion of k=xcexa3i=1L-12i-1xcex2k,i. These pseudo data symbols take on values in the set {xc2x11, xc2x1j} when the modulation index h equals xc2xd. In general, the first two pseudo data symbols, a0,n and a1,n can be written in an expanded form.                               a                      0            ,            n                          =                ⁢                  exp          ⁡                      (                          j              ⁢                              xe2x80x83                            ⁢              π              ⁢                              xe2x80x83                            ⁢              h              ⁢                                                ∑                                      m                    =                    0                                    n                                ⁢                                  xe2x80x83                                ⁢                                  α                  m                                                      )                                                            =                    ⁢                                    a                              0                ,                                  n                  -                  1                                                      ⁢                          J                              a                n                                                    ,                  a                      0            ,                          -              1                                                                        =                    ⁢          1                ,        J                                =                ⁢                              ⅇ                          jπ              ⁢                              xe2x80x83                            ⁢              h                                ⁢                      a                          1              ,              n                                                              =                ⁢                              a                          0              ,                              n                -                L                                              ⁢                      J                          α              n                                ⁢                      J                          α                              n                -                2                                              ⁢                      J                          α                              n                -                3                                              ⁢          …          ⁢                      xe2x80x83                    ⁢                      J                          α                              n                -                L                +                1                                                        
The set of pulse functions {hk(t)}, termed Laurent pulse functions, have a real value and are finite in duration, and are formed by an hk(t) equation.             h      k        ⁡          (      t      )        =            ∏              i        =        0                    L        -        1              ⁢          xe2x80x83        ⁢          c      ⁡              (                  t          +          iT          +                                    (                                                β                                      k                    ,                    i                                                  -                1                            )                        ⁢            LT                          )            
where       c    ⁡          (      t      )        =      (                                                                      sin                ⁡                                  (                                                            π                      ⁢                                              xe2x80x83                                            ⁢                      h                                        -                                          π                      ⁢                                              xe2x80x83                                            ⁢                                              hg                        ⁡                                                  (                                                      "LeftBracketingBar"                            t                            "RightBracketingBar"                                                    )                                                                                                      )                                            /                              sin                ⁡                                  (                                      π                    ⁢                                          xe2x80x83                                        ⁢                    h                                    )                                                      ,                                                              "LeftBracketingBar"              t              "RightBracketingBar"                        ≤            LT                                                            0            ,                                    elsewhere                    
Among these hk(t) pulses, most of the signal energy is carried by the principal Laurent pulse h0(t), which has a duration of L+1 bit times. Another property of the principal Laurent pulse h0(t) is that it is symmetrical about t=(L+1)T/2. The principal Laurent function h0(t) output provides a gross estimate of the transmitted symbol sequence. These properties of the principal Laurent pulse function h0(t) have not yet been exploited in developing the error signals for the symbol time and carrier phase tracking loops. These and other disadvantages are solved or reduced using the invention.
An object of the invention is to provide data aided symbol timing tracking in continuous phase modulation communication systems.
Another object of the invention is to provide data aided symbol timing tracking in a Gaussian minimum shift keying communications systems.
Yet another object of the invention is to provide data aided carrier phase tracking in continuous phase modulation communication systems.
Still another object of the invention is to provide data aided carrier phase tracking in a Gaussian minimum shift keying communications systems.
Still another object of the invention is to provide data aided carrier phase synchronizers and symbol time synchronizers in Gaussian minimum shift keying communications systems using principal Laurent responses for generating carrier phase and symbol time errors.
The present invention is directed to data aided synchronization in digital carrier phase and symbol timing synchronizers applicable to precoded continuous phase modulation (CPM) signal formats, such as in Gaussian minimum shift keying (GMSK) communications systems having, for example, a modulation index of xc2xd with a bandwidth time product (BT) of ⅕. The imbedded synchronizers enable simple implementations for data demodulation for CPM signals, such as GMSK signals with small BT values. Data aided tracking is applied in one form to symbol time tracking, and in another form, to carrier phase tracking. An advantage of the proposed data aided symbol timing synchronizer is the combination of both symbol timing tracking and data demodulation functions into an integrated process obviating the need for a separate data demodulator in the receiver. For example, for GMSK signals with BT values of ⅓ and larger, the data demodulation performance in the symbol timing synchronizer can provide optimum performance. An advantage of the data aided carrier phase synchronizer is the combination of both carrier phase tracking and data demodulation functions into one integrated process obviating a need for separate data demodulator in the receiver. For example, for GMSK signals with BT values of ⅓ and larger, the data demodulation performance provided by the carrier phase synchronizer can also be optimum.
In the first form, the symbol time tracking synchronizer includes a data aided symbol timing error discriminator that extracts the timing error of the received CPM signal from the principal Laurent amplitude modulation component by an early and late gating operation followed by a multiplication of the data decision to remove the data modulation in the error signal. This symbol timing error signal is then tracked by a second order digital loop operating at the symbol rate. In the second form, the carrier phase tracking synchronizer includes a data aided phase error discriminator that extracts the phase error of the received CPM signal from the principal Laurent amplitude modulation component by a cross correlation operation with the data decision produced by a serial data demodulator. This error signal is then tracked by a second order digital loop also operating at the symbol rate.
These digital synchronizers are used to track the symbol timing or carrier phase of a continuous phase modulation signal received in the presence of noise with the receiver operating in a data demodulation mode. These synchronizers have a nondegraded bit error rate (BER) performance with reduced design complexity. The GMSK signal with a BT=⅕ can be used as a typical partial response CPM signal. The hardware implementation of such a GMSK receiver with both synchronizers can be modeled for providing simulated BER performance. With data precoding of the original data bit stream prior to transmission of the CPM signal, the synchronizers can function as serial demodulators that achieve absolute phase data detection. The data precoding and data aided synchronization approach for detecting symbol timing and carrier phase error is central to providing accurate symbol time and carrier phase tracking in the synchronizers with reduced design complexity. These and other advantages will become more apparent from the following detailed description of the preferred embodiment.